When Jimmy Carr accused Jim Davidson of stealing a joke about fat women, it fell to fellow comic Stewart Lee to deliver the punchline. "If Jim Davidson can steal your material," said Lee, "then maybe it's time to rethink it." With that logic in mind, perhaps that's how comics Milton Jones and Lee Mack must be feeling this week, having had what they allege are their jokes tweeted to 36,000 online followers of that titan of standup comedy, Keith Chegwin.

The row reveals comedy's current panic about so-called joke theft, which intensifies with the advent of each new communication technology – mobile phones, YouTube and now Twitter. Chegwin says the contested jokes are his own, or old enough to be considered public property. When comedians cried foul, Chegwin branded them "jealous comics" and told them to lighten up. "If I do a gag [and] you nick it for yourself, good on ya," he tweeted. "So long as it gives people a chuckle. Life is too short."

Chegwin's laissez-faire attitude was the orthodoxy for much of comedy's history. Up to and including the Bernard Manning era, when comics more often worked regionally than nationally, and few featured on TV, jokes were swapped and copied at leisure. (With exceptions. In the early 20th century, the American entertainer WC Fields is said to have paid $50 to have a thieving comic's legs broken.) But with the advent of "alternative comedy", standup became something more personal. A comic needed his or her own identity; using someone else's gags was cheating.

These days, a comedian's jokes are his or her income. Comics slave over their gags, hone them, don't share them – and are loath to see them treated as public property. That's why They Think It's All Over star Lee Hurst went ballistic when he spotted an audience member recording his standup set on a mobile phone. (Hurst ended up with a fine for criminal damage, having pulverised the offending Motorola.) That's why Jay Leno, and several writers on his show, sued the author Judy Brown in 2006 for "writing" joke books filled with their gags.

But jokes are notoriously hard to copyright. Where does ownership reside? In the idea? The sequence of words? The mannerisms? And authorship is tricky to establish. Some of the best jokes are very simple – so simple that two comedians might easily write the same one. Topical jokes are particularly prone to overlap: witness the avalanche of identical wisecracks that flooded everyone's inbox when Michael Jackson died. One recent joke-theft row in the States centred on a quip about the wall being built to keep out Mexican immigrants. Several comics claimed authorship of the punchline, "Who's going to build it?". They may all have written it.

Comics such as Jones and Mack, Jimmy Carr and Tim Vine are uniquely vulnerable to joke theft. Their pithy one-liners are easy to recycle. An email was circulated in the 1990s that credited several of Vine's jokes to Tommy Cooper; Vine found himself rebutting the charge of plagiarism.

It's harder to steal jokes from raconteurs, character comics and observational acts. But even they are vulnerable now that a standup set might appear on YouTube the morning after its first performance. Jokes that were once circulated in pubs are now distributed to millions at the press of a key. Lightly regulated new media plus a hard-to-copyright artform equals an open goal for plagiarists. Comedians fear for their livelihoods. Irrespective of whose jokes they turn out to be, Chegwin's tweeting may indeed "give people a chuckle". But there's not much there for professional standups to laugh about.